Question

Butadiene (C4H6), the coefficients for the linear combination of atomic orbitals for the two lowest energy π-MOs are: Normalised Coefficients MO Atom 1 Atom 2 Atom 3 Atom 4 Wavefunction 2: +0.6015 +0.3717 -0.3717 -0.6015 Wavefunction 1: +0.3717 +0.6015 +0.6015 +0.3717 (i) Predict the coefficients at each atom for the two highest energy π-MOs (wavefunctions 3 & 4). Justify your solution using diagrams. (ii) Calculate the total π-electron densities on atoms 1, 2, 3, and 4. (iii) Calculate the total p-bond order between atoms 1-2, 2-3, and 3-4. (iv) Estimate the total σ- and π-bond orders between atoms 1-2, 2-3, and 3-4. (v) How does (iv) relate to the traditional representation of butadiene with a double-single-double bond structure. 

          Butadiene (C4H6), the coefficients for the linear combination of atomic orbitals for the two lowest energy π-MOs are:

Normalised Coefficients MO
Atom 1
Atom 2
Atom 3
Atom 4
Wavefunction 2:
+0.6015
+0.3717
-0.3717
-0.6015
Wavefunction 1:
+0.3717
+0.6015
+0.6015
+0.3717

(i) Predict the coefficients at each atom for the two highest energy π-MOs (wavefunctions 3 & 4). Justify your solution using diagrams.
(ii) Calculate the total π-electron densities on atoms 1, 2, 3, and 4.
(iii) Calculate the total p-bond order between atoms 1-2, 2-3, and 3-4.
(iv) Estimate the total σ- and π-bond orders between atoms 1-2, 2-3, and 3-4.
(v) How does (iv) relate to the traditional representation of butadiene with a double-single-double bond structure.
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Added by Matthew L.

Chemistry: Structure and Properties
Chemistry: Structure and Properties
Nivaldo Tro 2nd Edition
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Butadiene (C4H6), the coefficients for the linear combination of atomic orbitals for the two lowest energy π-MOs are: Normalised Coefficients MO Atom 1 Atom 2 Atom 3 Atom 4 Wavefunction 2: +0.6015 +0.3717 -0.3717 -0.6015 Wavefunction 1: +0.3717 +0.6015 +0.6015 +0.3717 (i) Predict the coefficients at each atom for the two highest energy π-MOs (wavefunctions 3 & 4). Justify your solution using diagrams. (ii) Calculate the total π-electron densities on atoms 1, 2, 3, and 4. (iii) Calculate the total p-bond order between atoms 1-2, 2-3, and 3-4. (iv) Estimate the total σ- and π-bond orders between atoms 1-2, 2-3, and 3-4. (v) How does (iv) relate to the traditional representation of butadiene with a double-single-double bond structure.
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Transcript

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00:01 Hello, so in this question we need to calculate the total p orbital bond order for 1 to 2, 2 to 3 and 3 to 4.
00:10 So we are going to calculate the pi bond order and formula to calculate bond order for pi with respect to j and k will be equal to summation of n i, t j and c k where n i will be the orbital occupancy of orbital, cj and ck will be the coefficients on j and k and for orbital i.
00:47 So the bond order for 1 to 2 will be equal to 2 times 0 .8717 times 0 .605.
01:03 Sorry, here it is 0 .3717.
01:07 So after solving this bond order for 1 to 2 comes out to be 0 .447.
01:15 And the total bond order will be total bond order will be equal to sigma number of sigma bonds plus number of pi bonds and that comes out to be 1 plus 0 .447.
01:32 That is 1 .447.
01:36 Now for bond order form 0 to 2 from 2 from 2 to 3 will be called...
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